Numerical methods for changing type systems

In this note we develop a numerical method for partial differential equations with changing type. Our method is based on a unified solution theory found by Rainer Picard for several linear equations from mathematical physics. Parallel to the solution theory already developed, we frame our numerical method in a discontinuous Galerkin approach in space-time with certain exponentially weighted spaces

The Proper Dissipative Extensions of a Dual Pair

Let A and B be dissipative operators on a Hilbert space H and let (A,B) form a dual pair, i.e. A ? B*, resp. B ? A*. We present a method of determining the proper dissipative extensions C of this dual pair, i.e. A ? C ? B* provided that D(A) ? D(B) is dense in H. Applications to symmetric operators, symmetric operators perturbed by a relatively bounded dissipative operator and more singular differential operators are discussed. Finally, we investigate the stability of the numerical range of the different dissipative extensions

A note on a two-temperature model in linear thermoelasticity

We discuss the so-called two-temperature model in linear thermoelasticity and provide a Hilbert space framework for proving well-posedness of the equations under consideration. With the abstract perspective of evolutionary equations, the two-temperature model turns out to be a coupled system of the elastic equations and an abstract ordinary differential equation (ODE). Following this line of reasoning, we propose another model which is entirely an abstract ODE.We also highlight an alternative method for a two-temperature model, which might be of independent interest

On some models in linear thermo-elasticity with rational material laws

In the present work, we shall consider some common models in linear thermo-elasticity within a common structural framework. Due to the flexibility of the structural perspective we will obtain well-posedness results for a large class of generalized models allowing for more general material properties such as anisotropies, inhomogeneities, etc